1.
Slides are available at
www.banhar.blogspot.com
Helping Students
Learn Mathematics
What & How of
Singapore Math
Dr. Yeap Ban Har
Marshall Cavendish Institute
Singapore
yeapbanhar@gmail.com
www.facebook.com/MCISingapore
2.
Synopsis
This course focuses on
teaching basic skills and
concepts including the four
basic operations – we will
see lessons on addition
(grade one) as well as
multiplication (grade two)
and division (grade three).
In addition, we will see a
lesson on division involving
fraction (grade five).
Dr. Yeap Ban Har
Marshall Cavendish Institute
Singapore
yeapbanhar@gmail.com
We will one example of
practice lesson (refer to the
green book). There is a
similar course that focuses
on problem solving.
3.
population = 5.3 million
area = 225 square miles
5.
“Upon separation from Malaysia in 1965, Singapore
was faced with … high levels of unemployment and
poverty. 70% of Singapore’s households lived in badly
overcrowded conditions, and a third of its people
squatted in slums on the city fringes. Unemployment
averaged 14%, GDP per capita was less than $2,700,
and half of the population was illiterate. “
6.
Score
1960-1970s
1980s
1990s
2000s
500’s
Japan
Hong Kong
Japan
Korea
Hong Kong
Japan
Korea
Singapore
Hong Kong
Japan
Korea
Singapore
400’s
Thailand
Philippines
Singapore
Thailand
Malaysia
Thailand
Malaysia
Thailand
Indonesia
Philippines
Indonesia
Philippines
300’s
| Hanusek, Jamison, Jamison & Woessmann 2008
7.
Country
GDP per capita in
current USD
2012
Singapore
60,800
Malaysia
16,800
Thailand
9,500
Indonesia
4,900
Philippines
4,400
Source | IMF
9.
What is Essential in Mathematics Literacy
Let’s look at what international assessment (PISA) for 15-year-olds and
Smarter Balanced Assessment for Hawaii State test suggest.
15.
Country
% of Low
Performers
% of High
Performers
Mean
Singapore
8.3
40.0
573
Vietnam
14.2
13.3
511
Thailand
49.7
2.6
427
Malaysia
51.8
1.3
421
Indonesia
75.7
0.3
375
OECD
23.1
12.6
494
| PISA 2012
16.
Country
% of Low
Performers
% of High
Performers
Mean
Shanghai
3.8
55.4
613
Singapore
8.3
40.0
573
Hong Kong
8.5
33.7
561
South Korea
9.1
30.9
554
Japan
11.1
23.7
536
Finland
12.3
15.3
519
OECD
23.1
12.6
494
| PISA 2012
24.
What is Essential in Mathematics Literacy
What should students be learning in mathematics and what are the
implications for classroom practices?
25.
What is Essential in Mathematics Literacy
What should students be learning in mathematics and what are the
implications for classroom practices?
communication
metacognition
number sense
visualization
patterns
27.
Summary of Oahu’s Discussion
Anchor Task
• Problem-solving Approach (Polya)
• Concrete – Pictorial – Abstract Approach (Bruner)
• Work in Groups and Talking (Vygotsky)
• Student-generated Ideas (Piaget)
• Progression from Literal to Abstract Ideas
• Questions for Self-directed Learning
Teacher Board Writing
Mini White Boards
Student Journal
• Promotes communication
• Allows for assessment
28.
Three-Part Lesson
Anchor Task
Guided Practice
Independent Practice
30.
What Does Teaching for Relational /
Conceptual Understand Look Like?
31.
Teaching for Meaning Making
Concrete Materials
Students are given
bags of 6 beans
each
Anchor Task
How many beans in
4 such bags?
Students Talking
Multiple Responses
Count all
Repeated addition
Multiplication
Board Writing
Student Journal
Meaning Making
4 x 6 is the same as 4 bags of
6 beans. Also linking new
materials (multiplication) to old
materials (addition).
32.
Teaching for Meaning Making
How do I know if I
have taught in a
meaningful way?
• Link to previous
knowledge
• Link to a
concrete
scenario
• Students can
extend their
thinking.
34.
Teaching for Meaning Making
Use of Textbooks
Suggest the kind of
anticipated
responses (add
another six, double,
associative
property and
subtraction
strategy)
As a reflection tool
for students at the
end of the
discussion (“Let’s see
how they do it.”)
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